When Will the Rabbit Population Recover After a Myxomatosis Outbreak?

In summary, exponential growth is a mathematical model that describes the rapid increase in quantity or size of a population, organism, or system over time. It differs from linear growth by involving a constant percentage change over time. The formula for exponential growth is y = ab^x and it can be affected by factors such as resource availability and environmental conditions. Exponential decay is the opposite of exponential growth and both are important concepts in understanding natural phenomena.
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A rabbit population satisfies the logistic equation dy/dt=2*10^-7y(10^6-y) where t is the time measured in months. The population is suddenly reduced to 40%of its steady state size by myxomatosis.
a) If the myxo' then has no effect how large is the population 8 months later?
b)How long will it take for the population to build up again to 90% of its steady state size?
 
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What have you tried so far? The first step will be to solve the differential equation to find the function y(t)
 

1. What is exponential growth?

Exponential growth is a mathematical model that describes the rapid increase in quantity or size of a population, organism, or system over time. It is characterized by a constant growth rate, resulting in a curve that becomes steeper and steeper as time goes on.

2. How is exponential growth different from linear growth?

Exponential growth differs from linear growth in that it involves a constant percentage change over time, whereas linear growth involves a constant numerical change over time. This means that exponential growth accelerates over time, while linear growth remains constant.

3. What is the formula for exponential growth?

The formula for exponential growth is y = abx, where y is the final quantity, a is the initial quantity, b is the growth factor or rate, and x is the time in periods.

4. What factors can affect the rate of exponential growth?

The rate of exponential growth can be affected by various factors such as the availability of resources, competition, environmental conditions, and the presence of limiting factors that can slow down or stop growth.

5. How is exponential decay related to exponential growth?

Exponential decay is the opposite of exponential growth, where the quantity or size decreases at a constant percentage rate over time. It follows the same formula as exponential growth, but with a negative exponent. Both exponential growth and decay are important concepts in understanding natural phenomena and making predictions in various fields of science.

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